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Testing the Correlated Random Coefficient Model

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  • James J. Heckman
  • Daniel A. Schmierer
  • Sergio S. Urzua

Abstract

The recent literature on instrumental variables (IV) features models in which agents sort into treatment status on the basis of gains from treatment as well as on baseline-pretreatment levels. Components of the gains known to the agents and acted on by them may not be known by the observing economist. Such models are called correlated random coefficient models. Sorting on unobserved components of gains complicates the interpretation of what IV estimates. This paper examines testable implications of the hypothesis that agents do not sort into treatment based on gains. In it, we develop new tests to gauge the empirical relevance of the correlated random coefficient model to examine whether the additional complications associated with it are required. We examine the power of the proposed tests. We derive a new representation of the variance of the instrumental variable estimator for the correlated random coefficient model. We apply the methods in this paper to the prototypical empirical problem of estimating the return to schooling and find evidence of sorting into schooling based on unobserved components of gains.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 15463.

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Date of creation: Oct 2009
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Handle: RePEc:nbr:nberwo:15463

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References

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  1. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, 05.
  2. Hansen, Karsten T & Heckman, James J & Mullen, Kathleen J, 2003. "The effect of schooling and ability on achievement test scores," Working Paper Series 2003:13, IFAU - Institute for Evaluation of Labour Market and Education Policy.
  3. Joseph Romano & Michael Wolf, 2003. "Exact and approximate stepdown methods for multiple hypothesis testing," Economics Working Papers 727, Department of Economics and Business, Universitat Pompeu Fabra.
  4. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  5. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
  6. James J. Heckman & Sergio Urzua & Edward J. Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," NBER Working Papers 12574, National Bureau of Economic Research, Inc.
  7. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
  8. Joshua D. Angrist & Guido W. Imbens, 1995. "Identification and Estimation of Local Average Treatment Effects," NBER Technical Working Papers 0118, National Bureau of Economic Research, Inc.
  9. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
  10. Griliches, Zvi, 1977. "Estimating the Returns to Schooling: Some Econometric Problems," Econometrica, Econometric Society, vol. 45(1), pages 1-22, January.
  11. Yitzhaki, Shlomo, 1996. "On Using Linear Regressions in Welfare Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 478-86, October.
  12. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  13. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
  14. James J. Heckman & Vytlacil, Edward J., 2007. "Econometric Evaluation of Social Programs, Part I: Causal Models, Structural Models and Econometric Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 70 Elsevier.
  15. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  16. Abbring, Jaap H. & Heckman, James J., 2007. "Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 72 Elsevier.
  17. Hidehiko Ichimura & Petra E. Todd, 2006. "Implementing Nonparametric and Semiparametric Estimators," CIRJE F-Series CIRJE-F-452, CIRJE, Faculty of Economics, University of Tokyo.
  18. James J. Heckman, 2001. "Micro Data, Heterogeneity, and the Evaluation of Public Policy: Nobel Lecture," Journal of Political Economy, University of Chicago Press, vol. 109(4), pages 673-748, August.
  19. James Heckman & Edward Vytlacil, 1998. "Instrumental Variables Methods for the Correlated Random Coefficient Model: Estimating the Average Rate of Return to Schooling When the Return is Correlated with Schooling," Journal of Human Resources, University of Wisconsin Press, vol. 33(4), pages 974-987.
  20. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267.
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Citations

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Cited by:
  1. Pedro Carneiro & James J. Heckman & Edward J. Vytlacil, 2010. "Estimating Marginal Returns to Education," NBER Working Papers 16474, National Bureau of Economic Research, Inc.
  2. Christian N. Brinch & Magne Mogstad & Matthew Wiswall, 2012. "Beyond LATE with a discrete instrument. Heterogeneity in the quantity-quality interaction of children," Discussion Papers 703, Research Department of Statistics Norway.
  3. Heckman, James J. & Schmierer, Daniel, 2010. "Tests of Hypotheses Arising in the Correlated Random Coefficient Model," IZA Discussion Papers 5205, Institute for the Study of Labor (IZA).
  4. James Heckman & Sergio Urzua, 2010. "Comparing IV with structural models: what simple IV can and cannot identify," CeMMAP working papers CWP08/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Dionissi Aliprantis, 2012. "When should children start school?," Working Paper 1126, Federal Reserve Bank of Cleveland.
  6. Salvador Navarro & Chao Fu & Steven Durlauf, 2012. "Capital Punishment and Deterrence: Understanding Disparate Results," 2012 Meeting Papers 53, Society for Economic Dynamics.

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